Time for action – inverting matrices

The inverse of a matrix A in linear algebra is the matrix A -1, which when multiplied with the original matrix, is equal to the identity matrix I. This can be written, as A* A -1 = I.

The inv function in the numpy.linalg package can do this for us. Let's invert an example matrix. To invert matrices, perform the following steps:

1. We will create the example matrix with the mat function that we used in the previous chapters.

   A = np.mat("0 1 2;1 0 3;4 -3 8")
   print "A\n", A

   The A matrix is printed as follows:

   A
   [[ 0  1  2]
    [ 1  0  3]
    [ 4 -3  8]]
   

2. Now, we can see the inv function in action, using which we will invert the matrix.

   inverse = np.linalg.inv(A)
   print "inverse of A\n", inverse

   The inverse matrix is shown as follows:

   inverse of A
   [[-4.5  7.  -1.5]
    [-2.   4.  -1. ]
    [ 1.5 -2.   0.5]]
   

   Tip

   If the matrix is singular or not square, a LinAlgError exception is raised. If you want, you can check the result manually. This is left as an exercise for the reader.

3. Let...